Librosa, STFT, zero-padding
Reference frequency
Fig. 3.3 Table 3.1 Fig. 3.4 Fig. 3.5
Maybe discussion of "tuning"
Maybe discussion of "compression"
In [1]:
import os
import numpy as np
import scipy
import matplotlib
from matplotlib import pyplot as plt
import librosa
import pandas as pd
import IPython.display as ipd
import music21 as m21
%matplotlib inline
Fig. 3.3¶
In [2]:
# read wav file
fn_wav = os.path.join('..', 'data', 'C3', 'FMP_C3_F03.wav')
x, Fs = librosa.load(fn_wav)
ipd.Audio(x, rate=Fs)
Out[2]:
In [3]:
# compute stft
N = 2048
N = 4096 * 4
H = 512
w = scipy.signal.get_window('hann', N)
X = librosa.stft(x, n_fft=N, hop_length=H, win_length=N, window=w, pad_mode='constant')
t = librosa.frames_to_time(np.arange(X.shape[1]), sr=Fs, hop_length=H, n_fft=N)
freq = librosa.fft_frequencies(sr=Fs, n_fft=N)
In [4]:
# plot stft
fig = plt.figure(figsize=(15, 5))
left = min(t)
right = max(t)
lower = min(freq)
upper = max(freq)
eps = np.finfo(float).eps
Y = 20 * np.log10(eps + np.abs(X) ** 2)
plt.imshow(Y, origin='lower', aspect='auto', cmap='gray_r', extent=[left, right, lower, upper])
plt.clim([-30, 30])
plt.ylim([0, 4500])
plt.xlabel('Time (seconds)')
plt.ylabel('Frequency (Hz)')
plt.colorbar()
# Create a Rectangle patch
rect = matplotlib.patches.Rectangle((30, 0.5), 1, 4490, linewidth=2, edgecolor='r', facecolor='none')
plt.gca().add_patch(rect)
Out[4]:
In [5]:
# pitch table
def F_pitch(p, a4_ref=440):
return 2 ** ((p - 69) / 12) * a4_ref
note_infos = []
for p in range(60, 73):
name = m21.note.Note(p).pitch.unicodeNameWithOctave
p_pitch = F_pitch(p)
p_pitch_lower = F_pitch(p - 0.5)
p_pitch_upper = F_pitch(p + 0.5)
bw = p_pitch_upper - p_pitch_lower
note_infos.append([name, p, p_pitch, p_pitch_lower, p_pitch_upper, bw])
df = pd.DataFrame(note_infos, columns=['Note', '$p$', '$F_\mathrm{pitch}(p)$', '$F_\mathrm{pitch}(p-0.5)$', '$F_\mathrm{pitch}(p+0.5)$', '$BW(p)$'])
html = df.to_html(index=False, float_format='%.2f')
html = html.replace('<table', '<table style="width: 66%"')
ipd.HTML(html)
Out[5]:
In [6]:
# definition of Y_lf
def F_coef(k, Fs, N):
return k * Fs / N
def P(p, Fs, N, a4_ref=440):
lower = F_pitch(p - 0.5)
upper = F_pitch(p + 0.5)
k = np.arange(N // 2)
k_freq = F_coef(k, Fs, N)
mask = np.logical_and(lower <= k_freq, k_freq < upper)
return k[mask]
def get_Y_lf(Y, Fs, N, a4_ref=440):
Y_lf = np.zeros((128, Y.shape[1]))
for p in range(128):
k = P(p, Fs, N, a4_ref)
Y_lf[p, :] = Y[k, :].sum(axis=0)
return Y_lf
In [7]:
# computation of Y_lf
Y = np.abs(X) ** 2
Y_lf = get_Y_lf(Y, Fs, N)
In [8]:
# plotting of Y_lf
fig = plt.figure(figsize=(15, 5))
left = min(t)
right = max(t)
lower = 0
upper = 128
plt.imshow(20 * np.log10(eps + Y_lf), origin='lower', aspect='auto', cmap='gray_r', extent=[left, right, lower, upper])
plt.clim([-30, 30])
plt.ylim([21, 108])
plt.xlabel('Time (seconds)')
plt.ylabel('Frequency (pitch)')
plt.colorbar()
# Create a Rectangle patch
rect = matplotlib.patches.Rectangle((30, 0.5), 1, 127, linewidth=2, edgecolor='r', facecolor='none')
plt.gca().add_patch(rect)
Out[8]:
In [9]:
# definition of C
def get_C(Y_lf):
C = np.zeros((12, Y_lf.shape[1]))
p = np.arange(128)
for c in range(12):
mask = (p % 12) == c
C[c, :] = Y_lf[mask, :].sum(axis=0)
return C
In [10]:
# computation of C
C = get_C(Y_lf)
In [11]:
# plotting of C
fig = plt.figure(figsize=(15, 5))
left = min(t)
right = max(t)
lower = 0
upper = 12
plt.imshow(20 * np.log10(eps + C), origin='lower', aspect='auto', cmap='gray_r', extent=[left, right, lower, upper])
plt.clim([0, 100])
plt.xlabel('Time (seconds)')
plt.ylabel('Chroma')
plt.colorbar()
plt.yticks(np.arange(12) + 0.5, [m21.note.Note(c).pitch.unicodeName for c in range(12)])
# Create a Rectangle patch
rect = matplotlib.patches.Rectangle((30, 0.0), 1, 12, linewidth=2, edgecolor='r', facecolor='none')
plt.gca().add_patch(rect)
Out[11]:
Fig. 3.5¶
In [12]:
# read wav file
fn_wav = os.path.join('..', 'data', 'C3', 'FMP_C3_F05.wav')
x, Fs = librosa.load(fn_wav)
ipd.Audio(x, rate=Fs)
Out[12]:
In [13]:
# compute stft
N = 2048
N = 4096
H = 512
w = scipy.signal.get_window('hann', N)
X = librosa.stft(x, n_fft=N, hop_length=H, win_length=N, window=w, pad_mode='constant')
t = librosa.frames_to_time(np.arange(X.shape[1]), sr=Fs, hop_length=H, n_fft=N)
freq = librosa.fft_frequencies(sr=Fs, n_fft=N)
# computation of Y_lf
Y = np.abs(X) ** 2
Y_lf = get_Y_lf(Y, Fs, N)
# computation of C
C = get_C(Y_lf)
In [14]:
fig = plt.figure(figsize=(15, 10))
# plot stft
plt.subplot(2, 1, 1)
left = min(t)
right = max(t)
lower = 0
upper = 128
plt.imshow(20 * np.log10(eps + Y_lf), origin='lower', aspect='auto', cmap='gray_r', extent=[left, right, lower, upper])
plt.clim([20, 50])
plt.ylim([55, 92])
plt.xlabel('Time (seconds)')
plt.ylabel('Frequency (pitch)')
plt.colorbar()
# Create a Rectangle patch
rect = matplotlib.patches.Rectangle((30, 0.5), 1, 127, linewidth=2, edgecolor='r', facecolor='none')
plt.gca().add_patch(rect)
# plotting of C
plt.subplot(2, 1, 2)
left = min(t)
right = max(t)
lower = 0
upper = 12
plt.imshow(20 * np.log10(eps + C), origin='lower', aspect='auto', cmap='gray_r', extent=[left, right, lower, upper])
plt.clim([20, 80])
plt.xlabel('Time (seconds)')
plt.ylabel('Chroma')
plt.colorbar()
plt.yticks(np.arange(12) + 0.5, [m21.note.Note(c).pitch.unicodeName for c in range(12)])
# Create a Rectangle patch
rect = matplotlib.patches.Rectangle((30, 0.0), 1, 12, linewidth=2, edgecolor='r', facecolor='none')
plt.gca().add_patch(rect)
plt.tight_layout()
Acknowledgment: This notebook was created by Frank Zalkow and Meinard Müller.
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